The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α ≥ 3/4. Existence on a long-time interval T* of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T* → ∞ as the frequency of gravity waves → ∞).
|Original language||English (US)|
|Number of pages||33|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - Oct 1999|
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics